Logical Reasoning and Deduction

Introduction

Imagine you're a detective. You arrive at a crime scene and find muddy footprints leading from the garden to the kitchen. The back door is open. A cake that was on the kitchen table is missing. What can you work out?

You might deduce: "Someone walked through the garden, entered through the back door, and took the cake." You didn't see it happen — but you used the evidence (the clues) to reach a logical conclusion.

This is logical reasoning — and it's one of the most important skills tested in the FSCE 11+ exam. In this lesson, you'll learn how to think logically, follow chains of reasoning, and avoid common thinking mistakes.

What Is Logical Reasoning?

Logical reasoning means using facts and rules to work out something new. You start with information you know (called premises) and use them to reach a conclusion.

Here's a simple example:

• Premise 1: All dogs are animals.
• Premise 2: Rex is a dog.
• Conclusion: Therefore, Rex is an animal.

This is called deduction — you deduce (work out) the conclusion from the premises. If the premises are true, the conclusion must be true.

If-Then Statements

Many logical arguments use if-then statements (also called conditional statements). These take the form:

If [something is true], then [something else follows].

For example:

• If it is raining, then the ground will be wet.
• If a number is even, then it can be divided by 2.
• If you don't study, then you won't be prepared for the exam.

graph LR
    A["IF condition is true"] --> B["THEN result follows"]
    B --> C["You can deduce the result"]
    A --> D["IF condition is NOT true"]
    D --> E["You CANNOT deduce anything"]
    style A fill:#e3f2fd
    style B fill:#e8f5e9
    style C fill:#e8f5e9
    style D fill:#fff3e0
    style E fill:#fce4ec

Important Rule: You Can't Go Backwards

If it is raining, then the ground is wet. But if the ground is wet, does that mean it's raining? No! Someone might have sprayed the garden with a hose. This is a very common logical mistake.

• Correct: It's raining, so the ground is wet. (Going forwards: IF to THEN)
• Incorrect: The ground is wet, so it must be raining. (Going backwards: THEN to IF — this is wrong!)

Logical Sequences

Sometimes you need to follow a chain of reasoning — a series of logical steps:

• If A is true, then B is true.
• If B is true, then C is true.
• Therefore, if A is true, then C is true.

Example:

• If it snows heavily, schools will close.
• If schools close, children will stay home.
• Therefore, if it snows heavily, children will stay home.

Flowchart for Logical Deduction

Use this process whenever you face a logical reasoning question:

graph TD
    A["Read the premises carefully"] --> B["Identify what you KNOW for certain"]
    B --> C["Ask: What MUST follow from this?"]
    C --> D{"Can I be 100% sure?"}
    D -->|Yes| E["This is a valid deduction"]
    D -->|No| F["This is only a possibility, not a certainty"]
    F --> G["Look for more information"]
    style A fill:#e3f2fd
    style E fill:#e8f5e9
    style F fill:#fce4ec

Common Logical Fallacies

A fallacy is a mistake in reasoning that seems right but is actually wrong. Here are some that you might encounter:

1. Assuming the Reverse

"If you eat too much sugar, you'll get a toothache. Sam has a toothache. Therefore, Sam ate too much sugar." Why it's wrong: Sam could have a toothache for many reasons — not just sugar.

2. Generalising from One Example

"My friend went to France and it rained every day. France always has bad weather." Why it's wrong: One trip doesn't tell you about the weather in an entire country.

3. Just Because Two Things Happen Together

"I wore my lucky socks and we won the match. My socks caused us to win." Why it's wrong: The socks had nothing to do with winning. Two things happening at the same time doesn't mean one caused the other.

4. Appeal to Popularity

"Everyone in my class thinks homework is pointless, so it must be." Why it's wrong: Just because many people believe something doesn't make it true.

Worked Examples

Worked Example 1: Simple Deduction

Premises:

• All Year 6 students at Oakwood School wear a blue jumper.
• Emily is a Year 6 student at Oakwood School.

Question: What can you deduce about Emily?

Answer: Emily wears a blue jumper.

Explanation: The first premise tells us that ALL Year 6 students at Oakwood wear blue jumpers. Emily is one of those students. So she must wear a blue jumper.

Worked Example 2: Chain of Reasoning

Premises:

• If the temperature drops below 0°C, water freezes.
• If water freezes on the roads, the roads become dangerous.
• If the roads become dangerous, the school bus cannot run safely.
• Tonight, the temperature will drop to -3°C.

Question: What can you deduce about the school bus?

Answer: The school bus cannot run safely.

Explanation: -3°C is below 0°C, so water will freeze. If water freezes on the roads, the roads become dangerous. If the roads are dangerous, the school bus cannot run safely. Each step follows logically from the one before.

Worked Example 3: Spotting a Fallacy